SAT II Math Episode 1 Part 9 potx

Mathematics Tests 155 ARCO ■ SAT II Math www.petersons.com/arco GO ON TO THE NEXT PAGE 4. Let R be the set of all numbers r such that –5 < r < 8. Let S be the set of all numbers s such that 3 < s < 10. The intersection, T, of R and S is the set of all numbers t such that (A) – 5 < t < 3 (B) – 5 < t < 8 (C) 0 < t < 8 (D) 3 < t < 8 (E) 8 < t < 10 5. If b > 1 and b y = 1.5, then b –2y = (A) – 3.0 (B) – 2.25 (C) (D) (E) 6. (y – 2) (y + 7) 2 < 0, if and only if (A) y < 2 (B) – 7 < y < 2 (C) y > – 7 (D) y < 2 and y ≠ – 7 (E) 2 < y < 7 and y > 7 7. A computer is programmed to add 3 to the number N, multiply the result by 3, subtract 3, and divide this result by 3. The computer answer will be (A) N + 1 (B) N + 2 (C) N (D) N – 2 (E) 8. where (x ≠ 5) = (A) (B) (C) (D) (E) none of these Part V156 www.petersons.com/arco ARCO ■ SAT II Math 9. If (A) (B) (C) (D) 1 (E) 10. (A) (B) (C) 3 (D) 1 (E) 3y – 1 11. If I varies inversely as d 2 and I = 20 when d = 3, what is I when d = 10? (A) 6 (B) (C) 18 (D) 1.8 (E) 12 12. If y is the measure of an acute angle such that sin , tan y = (A) (B) (C) (D) (E) Mathematics Tests 157 ARCO ■ SAT II Math www.petersons.com/arco GO ON TO THE NEXT PAGE 13. How many degrees between the hands of a clock at 3:40? (A) 150° (B) 145° (C) 140° (D) 135° (E) 130° 14. The legs of a right triangle are in the ratio of 1:2. If the area of the triangle is 25, what is the hypotenuse? (A) (B) (C) 10 (D) (E) 15. If , then x 2 – 2x + 1 equals (A) (B) 21− (C) 2 (D) (E) 16. A point is 17 in. from the center of a circle of radius 8 in. The length of the tangent from the point to the circle is (A) (B) 15 (C) 9 (D) (E) 17. In the formula , if C = 3 × 10 10 and L = 6 × 10 –5 , f = (A) 2 × 10 15 (B) 2 × 10 5 (C) 5 × 10 14 (D) 2 × 10 14 (E) 5 × 10 15 18. What is the approximate slope of the line 14 3 7 3 xy −= ? (A) 1.15 (B) 1.25 (C) 1.35 (D) 1.45 (E) 1.55 Part V158 www.petersons.com/arco ARCO ■ SAT II Math 19. How many numbers in the set {–8, –5, 0, 10, 20} satisfy the condition |x – 5|<11? (A) none (B) one (C) two (D) three (E) four 20. The graph of has its minimum value at which approximate value of x? (A) .83 (B) 1.12 (C) 1.21 (D) 1.35 (E) 2.47 21. In ∆ PQR, if the measure of ∠ Q is 50° and the measure of ∠ P is p°, and if is longer than , then (A) 0 < p < 40 (B) 0 < p < 80 (C) 40 < p < 80 (D) 80 < p < 90 (E) 80 < p < 130 22. Three parallel lines are cut by three nonparallel lines. What is the maximum number of points of intersection of all six lines? (A) 10 (B) 11 (C) 12 (D) 13 (E) 14 23. In figure 23, m∠ QSR = 30° in circle O. What is the measure of angle QPR? (A) 10 (B) 15 (C) 20 (D) 25 (E) cannot be determined from the information given Fig. 23 Mathematics Tests 159 ARCO ■ SAT II Math www.petersons.com/arco GO ON TO THE NEXT PAGE 24. If f(x) = x 3 –3 and g(x) = 7x–5, what is the approximate value of f(g(3.9))? (A) 389.23 (B) 938.32 (C) 4261.48 (D) 11086.57 (E) 14257.91 25. For what value(s) of y on the curve shown in figure 25 does y = 4x? (A) no value (B) +4 only (C) +3 only (D) –5 only (E) +4 and –12 26. In figure 26, is a diameter of the semicircle. If RS = 2 and ST = 3, then the area of the semicircle is (A) (B) (C) (D) (E) cannot be determined from the information given Fig. 25 Fig. 26 Part V160 www.petersons.com/arco ARCO ■ SAT II Math 27. A triangle with vertices (0, 0), (4, 3), and (–3, 4) belongs to which of the following classes? I—Scalene Triangles II—Isosceles Triangles III—Right Triangles IV—Equilateral Triangles (A) none (B) I only (C) II and III only (D) IV only (E) III only 28. The equation of the graph in figure 28 is (A) y = |x| (B) y = x (C) y = –x (D) y = 2x (E) y = x 2 29. What is the approximate length of the line segment joining the points N (7, –2) and J (–2, 7)? (A) 3.16 (B) 9.83 (C) 10.00 (D) 11.42 (E) 12.73 30. If the graph of the equation x + y – 8 + 4k = 0 passes through the origin, the value of k is (A) –2 (B) 2 (C) 0 (D) 1 (E) –1 Fig. 28 Mathematics Tests 161 ARCO ■ SAT II Math www.petersons.com/arco GO ON TO THE NEXT PAGE 31. If x = –8, the value of x 2/3 + 2x 0 is (A) –2 (B) 4 (C) –4 (D) 6 (E) –6 32. If , x = (A) 0 (B) 1 (C) –1 (D) 2 (E) –2 33. The equation expressing the relationship between x and y in the above table is (A) y = 2x + 1 (B) y = x + 2 (C) y = 2x – 1 (D) 2x + y = 7 (E) none of these 34. The graph of the equation x 2 – 2y 2 = 8 is (A) a circle (B) an ellipse (C) a hyperbola (D) a parabola (E) two straight lines 35. The fraction is equal to (A) (B) (C) (D) (E) Part V162 www.petersons.com/arco ARCO ■ SAT II Math 36. For what values of K does the equation Kx 2 – 4x + K = 0 have real roots? (A) +2 and –3 (B) –2 ≤ K ≤ 2 (C) K ≤ 2 (D) K ≥ –2 (E) –4 ≤ K ≤ 4 37. The radiator of a car contains 10 quarts of a 20% solution of alcohol. If 2 quarts of water are added, what percent of the resulting solution is alcohol? (A) 18% (B) % (C) % (D) 14% (E) % 38. Express the infinite decimal .212121 … as a common fraction. (A) (B) (C) (D) (E) 39. are tangent to circle O. If angle P measures 70°, how many degrees are in minor arc QT? (A) 140 (B) 125 (C) 120 (D) 110 (E) 100 Mathematics Tests 163 ARCO ■ SAT II Math www.petersons.com/arco GO ON TO THE NEXT PAGE 40. A cubic foot of water is poured into a rectangular aquarium with base 15 in. by 18 in. To what height in inches does the water rise? (A) (B) 6 (C) (D) (E) 5 41. A car drives a distance of d miles at 30 mph and returns at 60 mph. What is its average rate for the round trip? (A) 45 mph (B) 43 mph (C) 40 mph (D) mph (E) mph 42. If , what is the approximate sum of the roots? (A) 1.53 (B) 1.18 (C) –.65 (D) –.77 (E) –.85 43. A circle is inscribed in a triangle with sides 9, 12, and 15. The radius of the circle is (A) 2 (B) 3 (C) 3.5 (D) 4 (E) 4.6 44. The interior angles of a regular polygon are each 165°. How many sides does the polygon have? (A) 17 (B) 20 (C) 22 (D) 24 (E) 28 Part V164 www.petersons.com/arco ARCO ■ SAT II Math 45. Find the root(s) of the equation . (A) 11 (B) 4 (C) 4 and 11 (D) ±4 (E) none of these 46. Which of the following is the approximate equation of a line perpendicular to and passing through the point (A) (B) (C) (D) (E) 47. In how many points do the graphs of the equations x 2 + y 2 = 25 and y 2 = 4x intersect? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 48. In right triangle ABC, . If AB = 6, AC = 8, BC = 10, and DE = 4, find EC. (A) (B) (C) 5 (D) 6 (E) [...]... NEXT PAGE ARCO ■ SAT II Math www.petersons.com/arco Part V 16 6 PRACTICE TEST 1 Answer Key Math Level IC 1 2 3 4 5 6 7 8 9 10 E A E D D D B B C D 11 12 13 14 15 16 17 18 19 20 D B E A C B C B D B 21 22 23 24 25 26 27 28 29 30 B C E D E D C A E B 31 32 33 34 35 36 37 38 39 40 D E C C D B B E D A 41 42 43 44 45 46 47 48 49 50 C E B D B E C A D C SOLUTIONS 1 The correct answer is (E) The distributive principle... BD = x Then AD = 3BD or 12 + x = 3x Subtract x from both sides 3 The correct answer is (E) Examine each choice in turn (A) 19 n + 6: If n is even, 19 n is even, and the sum of two even numbers is even (B) 19 n + 5: If n is odd, 19 n is odd, and the sum of two odd numbers is even (C) 19 n2 + 5: If n is odd, n2 is odd, 19 n2 is odd, and the sum of two odd numbers is even (D) 18 n + 4: 18 n is always even, and... + 1 16 The correct answer is (B) Let the tangent PT = x; then OP = 17 and OT = 8 so that OPT is a right ∆ The radius by the Pythagorean Theorem www.petersons.com/arco ARCO ■ SAT II Math Mathematics Tests 17 1 17 The correct answer is (C) Substitute, When we divide powers of the same base, we subtract exponents 18 The correct answer is (B) 14 x − 3 y = 3 7 ⇒ 3 y = 14 x − 3 7 y= slope = 3 14 7 x− 3 3 14 ... there are 5 × 30° = 15 0° of arc Therefore at 3:40, the angle between the hands is 15 0° – 20° = 13 0° GO ON TO THE NEXT PAGE ARCO ■ SAT II Math www.petersons.com/arco 17 0 Part V 14 The correct answer is (A) Designate the legs of the right triangle by x and 2x The area of the triangle is then If the legs are 5 and 10 , the hypotenuse y is y 2 = 52 + 10 2 = 12 5 y = 12 5 = 25 ⋅ 5 = 5 5 15 The correct answer... ■ SAT II Math www.petersons.com/arco 16 8 Part V 9 The correct answer is (C) Multiply both sides by (r 1) Add S and –rL to both sides Divide both sides by S – L 10 The correct answer is (D) 11 The correct answer is (D) where K is the constant of proportionality To determine K, substitute I = 20 and d = 3 The formula then becomes Substitute d = 10 in the formula www.petersons.com/arco ARCO ■ SAT II Math. .. solution would be to list each of the 5 values of the given set in the inequality |–8 –5|=| 13 | = 13 , which is not less than 11 , etc 20 The correct answer is (B) The x value of the minimum point is x= ( ) 5 −b − − 5 = = ≈ 1. 12 2 2a 21 () GO ON TO THE NEXT PAGE ARCO ■ SAT II Math www.petersons.com/arco 17 2 Part V 21 The correct answer is (B) If PQ > PR, then m∠ R > m∠ Q, since the larger angle lies opposite... y = 3 7 ⇒ 3 y = 14 x − 3 7 y= slope = 3 14 7 x− 3 3 14 ≈ 1. 247 3 19 The correct answer is (D) |x – 5| < 11 is equivalent to x – 5 < 11 when x – 5 > 0 or x > 5 Thus x < 16 when x > 5 or 5 < x < 16 Only the value x = 10 in the given set is in this interval |x – 5| is equivalent to – (x – 5) when x – 5 < 0 or x < 5 Solving the inequality 5 – x < 11 , we get – x < 6 or x > – 6 when x < 5 Or – 6 < x < 5 The... even (E) 18 n + 5: 18 n is always even, and the sum of an even and an odd number is odd www.petersons.com/arco ARCO ■ SAT II Math Mathematics Tests 16 7 4 The correct answer is (D) Put both sets on a number line and determine their intersection The heavy line is the intersection of the sets 3 < t < 8 5 The correct answer is (D) These equalities follow from the laws of exponents Substitute by = 1. 5 6 The... of 4 It thus intersects the curve in (1, 4) and (–3, 12 ) Thus the desired values of y are +4 and 12 26 The correct answer is (D) Angle S is a right angle since it is inscribed in a semicircle Thus ∆RST is a right ∆ with RT the hypotenuse By the Pythagorean Theorem 27 The correct answer is (C) GO ON TO THE NEXT PAGE ARCO ■ SAT II Math www.petersons.com/arco 17 4 Part V 28 The correct answer is (A) The... the equation is y = |x| 29 The correct answer is (E) 30 The correct answer is (B) If the graph of the equation passes through the origin, the values x = 0, y = 0 must satisfy the equation Substitute 31 The correct answer is (D) Substitute –8 for x in x2/3+ 2x0 32 The correct answer is (E) Set the exponents equal 3x + 10 = –2x 5x = 10 x = –2 www.petersons.com/arco ARCO ■ SAT II Math . these Part V166 www.petersons.com/arco ARCO ■ SAT II Math PRACTICE TEST 1 Answer Key Math Level IC 1. E 2. A 3. E 4. D 5. D 6. D 7. B 8. B 9. C 10 . D 11 . D 12 . B 13 . E 14 . A 15 . C 16 . B 17 . C 18 × 10 –5 , f = (A) 2 × 10 15 (B) 2 × 10 5 (C) 5 × 10 14 (D) 2 × 10 14 (E) 5 × 10 15 18 . What is the approximate slope of the line 14 3 7 3 xy −= ? (A) 1. 15 (B) 1. 25 (C) 1. 35 (D) 1. 45 (E) 1. 55 Part. exponents. 18 . The correct answer is (B). 14 3 7 3 14 7 14 3 7 3 14 3 1 247 33 3 xy y x yx −= ⇒= − =− =≈slope . 19 . The correct answer is (D). |x – 5| < 11 is equivalent to x – 5 < 11 when